Linear approach for mathematical modelling as a tool for efficient portfolio selection

Abstract

This report introduces two approaches to the efficient portfolio selection problem, wherein the criteria and the constraints are linear with respect to control variables. The first approach consists of unconditioned optimization of the average expected efficiency value of a portfolio without imposing any additional constraints on the structure of selected portfolio. For this scheme the problem of effective portfolio formation is reduced to two linear programming problems, solving these for an efficient frontier may be effectively accomplished in closed form. The second scheme considers an additional set of group constraints, which can also be reduced to the problem of finding the Pareto fronts of two linear programming problems.